Sep 22, 2008 - robotics researchers but also by the leading automotive ... technology of torque-controlled lightweight robots (LWRs) developed during the past ...
Soft Robotics
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©PUNCHSTOCK
From Torque Feedback-Controlled Lightweight Robots to Intrinsically Compliant Systems € BY ALIN ALBU-SCHAFFER, OLIVER EIBERGER, MARKUS GREBENSTEIN, SAMI HADDADIN, CHRISTIAN OTT, € THOMAS WIMBOCK, SEBASTIAN WOLF, AND GERD HIRZINGER
Digital Object Identifier 10.1109/MRA.2008.927979
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IEEE Robotics & Automation Magazine
fter decades of intensive research, it seems that we are getting closer to the time when robots will finally leave the cages of industrial robotic workcells and start working in the vicinity of and together with humans. This opinion is not only shared by many robotics researchers but also by the leading automotive and IT companies and, of course, by some clear-sighted industrial robot manufacturers. Several technologies required for this new kind of robots reached the necessary level of performance, e.g., computing power, communication technologies, sensors, and electronics integration. However, it is clear that these human-friendly robots will look very different than today’s industrial robots. Rich sensory information, lightweight design, and soft-robotic features are required to reach the expected performance and safety during interaction with humans or in unknown environments. In this article, we will present and compare two approaches for reaching the aforementioned soft-robotic features. The first one is the mature technology of torque-controlled lightweight robots (LWRs) developed during the past decade at the German Aerospace Center (DLR) (arms, hands, a humanoid upper body, and a crawler). Several products resulted from this research and are currently being commercialized through cooperations with different industrial partners (DLR-KUKA LWR, DLR-HIT-Schunk hand, DLRBrainlab medical robot). The second technology, still a topic of worldwide ongoing research, is variable compliance actuation that implements the soft-robotic features mainly in hardware. We start by reviewing the main design and control ideas of actively controlled compliant systems using the DLR arms, hands, and the humanoid manipulator Justin as examples. We take these robots as a performance reference, which we are currently trying to outperform with new variable stiffness actuators. This leads us to the motivation of the variable stiffness actuator design. We present the main design ideas and our first results with the new actuator prototypes. Some experimental examples providing first validation of the performance and safety gain of this design approach are presented finally.
Mechatronic Design of LWR with Joint Torque Sensing In this section, a mechatronic design approach for obtaining the robots with the desired lightweight and performance properties is briefly described. The following aspects are of particular relevance. u Lightweight structures: lightweight metals or composite materials are used for the robot links. u High-energy motors: In contrast to industrial robots, motors with high torque at moderate speed, low energy loss, and fast dynamic response are of interest rather than high-velocity motors. For this purpose, special motors, namely, the DLR Robodrive, have been designed. u Gearing with high load to weight ratio: Harmonic drive gears are used for the DLR robots. 1070-9932/08/$25.00ª2008 IEEE
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Integration of electronics into the joint, leading to a modular design: This allows the design of robots of increasing kinematic complexity based on integrated joints as in the case of the DLR humanoid Justin. Moreover, one obtains a selfcontained system, which is well suited for autonomous, mobile applications. u Full-state measurement in the (a) (b) (c) joints: As will be outlined in the ‘‘Compliance Control for Lightweight Arms’’ section, our robots use torque sensing in addition to position sensing to implement a compliant behavior and a smooth, vibration-free motion. The full-state measurement in all joints is performed at 3-kHz cycle (d) (e) (f) using strain-gauge-based torque-sensors, motor position sensing based on mag- Figure 1. Overview of the DLR Robots. (a) The DLR-LWR-III equipped with the DLR-Hand-II. (b) The netoresistive encoders, and DLR-KUKA-LWR-III that is based on the DLR-LWR-III. (c) The DLR humanoid manipulator Justin. (d) link side position sensors The DLR-Hand-II-b, a redesign of the DLR-Hand-II. (e) The DLR-HIT hand, a commercialized version based on potentiometers of the DLR-Hand-II. (f) The DLR-Crawler, a walking robot based on the fingers of the DLR-Hand-II. (used only as additional of energy shaping to the feedback of the different state vector sensors for safety considerations). components. u Sensor redundancy for safety: Positions, forces, and u A physical interpretation of the joint torque feedback torques are redundantly measured. loop is given as the shaping of the motor inertia. These basic design ideas are used for the joints in the arms, u The feedback of the motor position can be regarded as hands, and torso of the upper body system Justin (Figure 1). shaping of the potential energy. Moreover, because the joints are self-contained, it is straightforward to combine these modules to obtain different kinematic configurations. For example, the fingers have been used Link Position Sensor to build up a crawler prototype. Figure 2 shows the exploded Cross Roller Bearing view of one LWR-III (DLR-LWR-III) joint. u
Compliance Control for Lightweight Arms In the next two sections, the framework used to implement active compliance control based on joint torque sensing is summarized. The lightweight design is obtained by using relatively high gear reduction ratios (typically 1:100 or 1:160), leading to joints that are hardly backdrivable and have already moderate intrinsic compliance. Therefore, we model the robot as a flexible joint system. Thus, measuring the torque after the gears is essential for implementing high-performance soft-robotic features. When implementing compliant control laws, the torque signal is used both for reducing the effects of joint friction and for damping the vibrations related to the joint compliance. Motor position feedback is used to impose the desired compliant behavior. The control framework is constructed from a passivity control perspective by giving a simple and intuitive physical interpretation in terms SEPTEMBER 2008
Power Converter Unit Joint- and Motorcontroller Board Power Supply
Torque Sensor with Digital Interface Harmonic Drive Gear Unit DLR RoboDrive with Safety Brake and Position Sensor Carbon Fiber Robot Link
Figure 2. The mechatronic joint design of the DLR-LWR-III, including actuation, electronics, and sensing.
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Joint Torque Control: Shaping the Actuator Kinetic Energy To simplify the analysis and to be able to generalize the joint level approach also to Cartesian coordinates, the idea of interpreting the joint torque feedback as the shaping of the motor inertia plays a central role [1], [2]. It enables one to directly use the torque feedback within the passivity framework and conceptually divides the controller design into two steps. One is related to the torque feedback and the other to the position feedback (Figure 3). As sketched in the figure and presented in detail in [1] and [2], the torque control feedback reduces the motor inertia to a value Bh, lower than the real value B. (Although friction is not depicted in Figure 3, note that the frictional effect will be reduced by the same factor B1 h B.) Motor Position-Based Feedback: Shaping the Potential Energy Using motor position h for control, and not the link position q, is essential for the passivity properties of the controller. However, the desired position and stiffness are usually formulated in terms of the link position. For the impedance controllers of the DLR LWRs, the position feedback has the form u¼
@VP (q(h)) Dh h_ þ g(q(h)), @h
(1)
with u being the input to the torque controller, VP a positive definite potential function, and Dh a positive definite damping matrix chosen for a well-damped transient behavior [3]. This is the classical structure of a compliance controller for rigid robots, except for the fact that, instead of the link position q, a position signal q(h) is used, which is statically equivalent to q, i.e., q(h) ¼ q if q_ ¼ h_ ¼ 0 and can be computed numerically [1], [2]. (In practice, we often use the trivial approximation q(h) ¼ h for applications in which high position accuracy is not required.) Because now the position feedback is again only a function of h, the passivity of the controlled robot is given with respect to the input-output pair (sext , q_ ) (Figure 3). To obtain a joint level impedance controller, one can simply use VP (q) ¼ 12 (qd q)T KJ (qd q), whereas for Cartesian
Impedance u Law g(q) θ
Torque Control τm τ, τ
τa
K Bθ D
q
Dynamics Passive Subsystem q(θ)
Rigid Robot τext Dynamics
Passive Environment
Figure 3. Representation of the compliance-controlled robot as a connection of passive blocks. h is the motor position, and q the link position. B, K, and D are the motor inertia, joint stiffness, and damping matrices, respectively. s is the elastic joint torque, sa the total (elastic and damping) joint torque, sext the external torque, and g the gravity torque. 22
impedance control, VP is defined as a function of the Cartesian coordinates x(q), as detailed in the following section. The external torque sext is then replaced by the external force F ext. (The relation between the external tip force F ext and the external joint torque sext is sext ¼ J(q)T F ext .) A Lyapunov function for the system is obtained by summing the kinetic and the gravitypotential energy of the rigid part of the robot dynamics with the kinetic energy of the scaled motor inertia and the potential energy of the controller [1], [2].
Impedance Control for Complex Kinematic Chains In this section, we show how to apply the impedance control concept from the previous section to kinematically more complex robot systems, like artificial hands and anthropomorphic two-handed manipulator systems. The design of appropriate potential functions VP (q) is discussed in this section. Furthermore, we will assume the potential function Vs of a virtual spatial spring, e.g., the ones designed in [4]–[6], as a basic building block. This potential function Vs (H 1 , H 2 , K) depends on two frames H 1 2 SE(3) and H 2 2 SE(3), between which the spring is acting, and also on some configuration-independent internal parameters K, like the stiffness values or the rest length. Artificial Hands Similar to the DLR lightweight arm, the DLR-Hand-II is equipped with joint torque sensors in addition to joint position measurements. Therefore, it is possible to apply the impedance control aspects as presented in the previous section to our anthropomorphic robot hand. The feedback of the torque sensors is used to increase the backdrivability, respectively the sensitivity, of the joints. Because of the small link masses and the high mechanical joint stiffness, vibration damping is not an issue here. Therefore, the approximation q ¼ h ¼ q can be made. While joint and Cartesian impedance control are used for power grasp and independent fingertip motion, respectively, the most interesting case from a control point of view is the fine manipulation of a grasped object as all degrees of freedom (DoF) of the hand can contribute to its motion. In this case, the combined system containing arm, hand, and object represents a parallel robot (Figure 4). The task coordinates consist of two contributions. On the one hand, the Cartesian coordinates of the grasped object and, on the other hand, the coordinates that are related to internal forces. In [7], we introduced a passivity-based object-level controller for a multifingered hand based on a virtual object similar to [8]. In contrast to the intrinsically passive controller (IPC) [8], the object frame is defined uniquely by the i ¼ 1 . . . N Cartesian fingertip positions pi (q) by an appropriate kinematic relationship. The definition is such that it enables the spanning of the null space of the grasp matrix by internal forces generated by virtual elastic elements connecting the virtual object frame with the fingertips (Figure 4). The definition of a potential function VP (q) to derive at an object-level controller is then described by the superposition of two potentials: the potential of a spatial spring Vs (H ho (q),
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H ho, d , Kho ) between the virtual object frame H ho (q) and a virtual equilibrium frame H ho, d and a potential Vhc (q, Khc ) describing the ith spring connecting the virtual object with the ith frame of the fingertips H f , i (q) for i ¼ 1 . . . N that are used to generate internal forces, i.e., VP (q) ¼ Vs (H ho (q), H eq , Kho ) þ Vhc (q, Khc ):
(2)
The expressions Kho and Khc contain the stiffness matrix of the spatial spring and the coupling spring parameters, respectively. The potential for the coupling springs is different from the potentials for spatial springs and is chosen to be spherical for each fingertip i [7]. Vhc (q, Khc ) ¼
N 1X Khc, i ½kDpi (q)k li, d 2 , 2 i¼1
(3)
with Dpi (q) ¼ pi (q) pho (q) being the distance from the position of the fingertip frame i to the virtual object frame position pho , lI;d the desired rest length, and Khc;i > 0 the corresponding coupling stiffness. Employing Impedance Control for Two-Handed Manipulation A natural extension of the impedance control approaches for the arms and hands allows one to formulate intuitive compliance behaviors also for more complex anthropomorphic manipulators like the humanoid manipulator Justin [Figure 1(c)]. This system was built at DLR as a test bed for studying two-handed manipulation tasks. It consists of two four-fingered artificial hands, two lightweight arms, and a sensor head mounted on a movable torso including the neck. Overall, Justin has 43 DoF. Let us first consider the problem of controlling two arms. The end-effector frames of the right and left arm will be denoted as H r (q) and H l (q), respectively. Similar to multifingered hands, the compliance control of two arms has to handle the interaction forces between the two arms as well as the forces that the two arms exert cooperatively on the environment. The implementation, however, is even simpler in this case and can be done by combining two spatial springs. One spatial spring defines the relative compliance between the arms and can be described in a straightforward way by the potential function Vs (H r (q), H l (q), Kc ). For implementing the cooperative action of the two arms, it is useful to rely on a virtual object frame H o (H r (q), H l (q)) depending on the two end-effector frames of the right and left arm. This object frame describes a relevant pose in between the arms (usually just the mean between the pose of the right and left arm) and thus represents the pose of a grasped object. This virtual object is then connected via a spatial spring Ko to a virtual equilibrium pose H o, d . In combination with the coupling stiffness, one can thus intuitively define an impedance behavior that is useful for grasping large objects with two arms. The resulting potential function is given by VP (q) ¼ Vs (H o (H r (q), H l (q)), H o, d , Ko ) þ Vs (H r (q), H l (q), Kc ): SEPTEMBER 2008
(4)
In case of a two-handed system, such a compliance behavior can easily be combined with the object-level compliance potentials designed for artificial hands. Therefore, the virtual viscoelastic springs are now attached to the virtual object frames H r, o (q) and H l, o (q) of the hands instead of attaching them directly to the end effectors of the arms (Figure 5). In combination with the interconnection potentials Vhcr (q, Khcr ) and Vhcl (q, Khcl ) for the right and left hand, the complete potential function is now given by VP (q) ¼ Vs (H o (H r, o (q), H l, o (q)), H o, d , Ko ) þ Vs (H r, o (q), H l, o (q), Kc ) þ Vhcr (q, Khcr ) þ Vhcl (q, Khcl ):
(5)
Note that all spatial springs generate joint torques for the arms, hands, and torso by computing the total derivative of the potential function with respect to the generalized coordinates of the complete mechanism [c.f. (1)]. The presented control approach results in a passive closed-loop system by design, and it is therefore related to other intuitive passivity-based control approaches like the IPC
∂Vs ∂q
Khc,3 Khc,4
x
Kho
x
Hho(q) Khc,2 Khc,1
Hho,d
Figure 4. DLR-Hand-II superimposed by the virtual springs defined by the potential functions in (2) and the virtual object.
Kc
Ho(q)
Ko Ho,d
Figure 5. Two-hand impedance behavior by combining the object-level impedances of the hands and the arms.
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[8]. Moreover, the chosen set of virtual spatial springs allows for a conceptually simple physical interpretation and consequently for an intuitive parametrization in any higher-level planning stage.
Adjusting the Mechanical Compliance: Motivation of the Variable Stiffness Actuator Design From Actively Controlled to Passive Compliance The paradigm of torque-controlled LWRs was presented in some detail up to now. Various robot examples and the underlying control concepts were introduced. On the basis of the experience gained with this successful approach, we were also trying to identify its limitations and recognize new directions of research for further increasing the performance and safety of robots. The limitations of the achievable compliance by active control especially becomes an issue when considering the protection of the robot joint from external overload [9]–[11]. (This is due to the limited sensor precision, model accuracy, and sampling time as well as the motor saturation.) This threat can be diminished by deliberately introducing mechanical compliance into the joint. Furthermore, future robotic systems are supposed to execute tasks with similar speed and dexterity to humans. Extreme examples show that humans are capable of generating enormous joint speeds such as shoulder rotation of 6,900 9,800=s during a baseball pitch of a professional player [12]. This speed range is currently not realizable by robots if the torque range and the weight of the joint should also be compatible with human values. Therefore, new actuation concepts are sought for so as to approach such requirements. The concept of variable stiffness actuation (VSA), or its generalization of variable impedance actuation (VIA), seems to be a promising solution in this context, and its design and control was addressed in numerous publications [9], [13]–[16]. An elastic element in the joint serves as an energy storage mechanism, possibly decreasing the energy consumption of the entire system during the task execution, e.g., when playing drums or during running. Furthermore, the stored energy can be used to considerably increase the link speed as exemplified in the
Figure 6. The integrated DLR hand-arm system.
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‘‘Throwing’’ section. In contrast to the active compliance case, the robot remains compliant even in the case of deactivation or malfunction of the joint, thus potentially increasing the safety of humans interacting with the robot and protecting the robot joint from external impacts. Our goal is, based on our experience with torquecontrolled LWRs, to built up a fully integrated VSA hand-arm system (Figure 6) for a close, safe, and performant interaction with humans while fulfilling the aforementioned requirements as close as possible. Naturally, such a fundamental paradigm shift comes at a certain cost. The increased number of actuators and the small intrinsic damping are certainly some of the major challenges in controlling a variable compliance joint. (Introducing mechanical damping into the system would increase the open-loop performance at the cost of higher complexity, weight, and energy losses.) The expected reduction in absolute position accuracy because of the elasticity needs to be compensated for high precision tasks by external sensing, e.g., vision. Furthermore, a lower mechanical bandwidth will result from the generally lower joint stiffness. Regarding the realizable compliance, the first prototypes are expected to implement a diagonal joint stiffness matrix only. This is posing some limitations on the structure of the achievable Cartesian compliance [17]. However, if necessary, the couplings can still be obtained by active control as described in the ‘‘Compliance Control for Lightweight Arms’’ and ‘‘Impedance Control for Complex Kinematic Chains’’ sections. To exemplify some possible advantages of the VSA design, a preliminary discussion of the influence of joint compliance on human and robot safety is presented before introducing the hardware design in the ‘‘New Hardware Design Concepts’’ section. Protecting the Robot Joint and the Human by Variable Joint Stiffness Rigid impacts at high speeds pose an enormous threat to the robot joint [11]. The exceedance of the maximum nominal joint torques is already shown at less than half of the maximum speed of the DLR-LWR-III. This problem necessitates fast collision detection and reaction schemes to prevent damage to the manipulator. (Results from [27] indicate that this is only possible up to a certain impact velocity that is far below the maximum velocity of the manipulator. Especially, the jointtorque sensor and the gears can be severely damaged.) In contrast, the VSA actuators limit in an intrinsic way the impact joint torques by elastically decoupling the link from gearbox and motor for the duration of the impact. To visualize this effect, a one-dimensional translational example (Figure 7) was simulated. In Figure 8, the joint force FSpring during an impact with a human head at 2 m/s for a variable stiffness (VS) joint is depicted. One can see that it decreases dramatically for a joint stiffness reduced by one or two orders of magnitude compared with the DLR-LWR-III, thus substantially reducing the load of the joint. First experimental results confirming the aforementioned statements are shown in the ‘‘Experimental Validation of Joint Overload Protection’’ section.
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q˙
θ˙ Fd
3,000 2,000 1,000 0
0
0.1
0.2
0.3 Time t[s]
0.4
HIC = 28.8 KSpring = 0.1KLWR-III 0
0.1
0.2
0.3 Time t[s]
0.4
HIC = 28.8 KSpring = 0.01KLWR-III 0
0.1
0.2
0.3 Time t[s]
0.4
0.5
Fext FSpring
q
Fext
Fext FSpring
FSpring [N]
0.5
Figure 8. Effect of joint stiffness reduction on impact force, HIC, and spring force during an impact with the human head at 2 m/s impact velocity. The spring force decreases in magnitude and increases in duration when lowering the spring stiffness. The joint stiffness KSpring was chosen to be KLWR-III , 0:1 KLWR-III , and 0:01 KLWR-III , i.e., 100%, 10%, and 1% of the reflected DLR-LWR-III joint stiffness.
Blade
x˙R
xH
Figure 7. 1-DoF model of the impact between a VS robot and a human. The robot is modeled as a mass-spring-mass system, representing the motor mass, joint stiffness, and link mass. The human model is a Hunt-Crossley model harmonized with experimental crash test dummy data [11]. B, M were selected to be the reflected inertias in case of a typical stretched out collision configuration with the DLR-LWR-III, and KSpring varied according to Figure 8.
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400 300 200 100 0
0.5
x˙R FSpring
400 300 200 100 0
MH
M θ
400 300 200 100 0
FSpring [N]
3,000 2,000 1,000 0
HIC = 28.8 KSpring = KLWR-III
Fext FSpring
FSpring [N]
Fext [N] Fext [N]
3,000 2,000 1,000 0
KH
KSpring
B
We are getting closer to the time when robots will finally leave the cages of industrial robotic workcells.
Fext [N]
The possible injury of the human during such rigid impacts is discussed in detail in [11] and [18]. It is shown there that the impact forces (which are mainly related to the impact velocity), and thus the potential injury of a human, do not depend on the joint stiffness already for link inertias and joint stiffness similar to the ones of the DLR-LWR-III. In Figure 8, the head injury criterion (HIC) and the impact forces Fext are depicted, showing that even with reduced joint stiffness, they basically stay the same. This can be explained by the fact that rigid impacts are practically over before the joint force starts rising. In other words, it is only the link inertia involved in such hard and rigid impacts. A case for which compliance of the robot does reduce the injury risk for humans is given by impacts with sharp tools at moderate velocity. This is exemplified by the experiment from Figure 9, in which the DLR-LWR holding a knife moves along a desired trajectory in position or joint impedance-controlled mode, penetrating a silicone block. Figure 10 shows that with very low joint stiffness, the force and penetration depth increase much slower. For this particular trajectory, one presumably could prevent damaging the human skin. (Already contact forces of
